Repeated prisoner’s dilemmas with errors: how much subgame-perfection, how much forgiveness, and how much cooperation?

We consider the repeated prisoner’s dilemma with implementation errors, and look at the resulting population dynamics, both analytically and with simulations. We show that with implementation errors, pure equilibrium strategies represented by finite state automata exhibit a structure that we call self-mirroring. Because selection easily spreads thinly on subgames that are reached after (multiple) errors, we find that in the simulations, strategies are often not best respond- ing in all subgames. We also explore how forgiveness and cooperation respond to changes in the error rate and the continuation probability. Close to an error rate of 0, both show a hump-shaped pattern. We also explore how forgiveness and cooperation change with the error rate in models with a limited strategy set, and we have results for forgiveness at high error rates and/or low continuation probabilities.